Rating: 
Summary: This is Linear Algebra?
Review: First I must say that i have not taken any other course in Linear Algebra then the course I took with this book. Further, I must say I am reviewing this book with the perspective of someone who is major in mathematics with the possible eye to graduate school in the subject.
However, regardless of my lack of exposure elsewhere, I have started to read other books in the topic, and I had the benefit of having a very formal instructor in the class I was in. This book seems to be the standard for the non-honors 2nd or 3rd year Linear Algebra course.
I have several problems with this text. My first is the fact that it is quite informal in organization. The course I was taught in asked more theoretical questions in exam and lecture and was attempting to imprint, in the student, a sense of understanding more so then the 'intuitive' or 'common sense' perspective that was displayed by Lay (a good example of this is Lay's "geometric" paradigm of Linear Algebra which he conveys throughout the book).
I have several problems with this book,
1. The book is not versatile in its display of the material. What I mean by this is that the book uses a very algorithimic method of introducting theorems and topics. I must point out also, that it operates almost exlusively in the finite vector space setting. I believe the student does not get the full grasp of the power of Linear Algebra to be applied to more things then vector spaces. Hence, the appropriate use of the book is nesscairly limited to those classes that teach students whose sole aim is to understand the applications of Linear Algebra, and not the topic itself.
2. The excercises were trivial and laughable as preperation for the exams I took. I do not lay blame on my instructor as I have heard that this book was adequate for a number of other sections in my university. However, I must add that the questions I was asked, in my opinion, truly tested whether the student understood the theory and thus the nature of the subject. Yet, I found it very unfortunate that neither the excercises nor the exposition were at all adequate for preperation for my exams.
3. My final problem with the book is the nature of its organization. I can't say how many times the book proved something using induction or some other constructivist method when it could have been proven using far more eloquent techniques and would have been able to convey deeper principles and thus greater understanding of the topic. Again, I know this is true, becuase the instructor conveyed these alternative techniques to us in lecture, thus I was able to see both perspectives.
I do not want to be completely biased in this review (although this is the nature of reviews in general). The book has several good points, one of which that it does come with an excellent student manaul, that does contain well written solutions to the odd problems. Further, the solution manaul is moderatly priced (less then $20.00 USD). Also, the book contains many problem sets, which may be appropriate in some classes, but not so much in others (I realize this is a dependent on instructor temperment).
In conclusion it would have been faulty on my part if I had given this book less then 3 stars, because as stated above, it is probably appropriate for many classes, however, in my exposrue to the text, in my circumstances, it failed miserably, thus I believe, the book has failed in my case and probably many other cases similiar to mine.
Rating: 
Summary: Not bad for a math book!
Review: As a college student, I'm really no fan of reading my math texts; often they're incomprehensible and frustrating. But this text is clear and understandable. The only thing I find aggravating is the lack of help given on the true/false problems - even the study guide seems lacking in this area.
Rating:
Summary: Not bad for a math book!
Review: As a college student, I'm really no fan of reading my math texts; often they're incomprehensible and frustrating. But this text is clear and understandable. The only thing I find aggravating is the lack of help given on the true/false problems - even the study guide seems lacking in this area.
Rating: 
Summary: A great book.
Review: Because Dr. Lay's book is so well written, linear algebra turned out to be the easiest course I took in my undergraduate work.Lay's book is clear, concise, and overall very well-done. His writing is great; he explains each derivation. The problems he sticks in at the end of the chapter to check your understanding are really nice. The study guide is also very helpful. I wish there were more textbooks like this one.
Rating: 
Summary: This book sucks.
Review: By far the worst texbook that I have ever had the misfortune to be assigned. I had to drop the course because of it. The language requires a translator to interpret, the problems are presented in an unclear manner, and worst of all, you cannot verify whether your answers are correct, because the book tells you that you should already know them. Avoid this book at all costs. I recommend any book by Robert Busby.
Rating:
Summary: beware, this book drain your intelligence
Review: confusing, discouraging, boring, wordy, non applicable math books made to distract natural human intelligence to the fullest, smells like state uni bathroom
Rating:
Summary: A thorough and concise textbook.
Review: Dr. Lay has put out a quality textbook, worthy of a read as well as a series of challenging questions. As an undergraduate physics student at Queen's University, it is often frustrating when the course materials are lacking in study content. This is not the case with this book. The only real drawback to this textbook is the limitation of the study guide that accompanies the book. When preparing for exams, it is often best to review extra problem that were not assigned throughout the year, since it is not possible to confer with the professor or the TA with regards to every question. One must complete this task independently. Dr. Lay's student guide an excellent reference pertaining to the problems that it contains solutions for, however some the challenging study questions require a more in depth analysis than is provided. On the whole this textbook is worth while reference and definitely worth considering for and undergraduate course in linear algebra. A.C. Toews (Queen's Arts & Science 2001)
Rating: 
Summary: Too much theory, and confuses vectors with matrix operations
Review: Honestly, I would have never known that there was a better way to do this if I hadn't had to drop this class last fall for medical reasons, then retake it this spring with different prof. and different book. This d____ed book goes out of its way to make things confusing, causing too much memorization, and intertwines what a vector space is with matrix operations. It really does not have to be this confusing. Further, the guy does not teach you how to do proofs, but then requires you to do them in homework. He doesn't teach you where to start from, or what to think of when doing a proof. Linear Algebra is a tough class to begin with. It is known to be abstract and theoretical. Lay does not need to make an already challenging subject more challenging by presenting it in such a confusing way. Thank God I had to drop last fall. I'd have gotten a C or a D (and I'm a straight A student) if I'd had to stick with the Lay book.
Rating:
Summary: Outstanding linear algebra text !!
Review: I am currently about a week away from completing a course in which we've used this next (the THIRD edition). I cannot express enough the unbelievable level of quality and attention to instruction that has been put into this edition. I cannot speak for previous editions, and from some of these comments it doesn't sound as those past versions of the text are anywhere near as good as the third edition. For what it's worth, I strongly suggest that anyone needing a secondary text for a linera algebra course consider this book. It may be pricey, but there's no way I'm letting this one go after the semester is over. It's going on my shelf and staying there! This book has more visual, geometric interpretations and depictions that you'd ever find in another book, and what's more it's actually concise. You don't get 10 pages of explanation when one or two will suffice. Concepts are continually reinforced and re-examined, not to mention built upon. You will continuously be presented with the links between chapters and concepts, and this is one of the book's greatest strengths. When you get to see how it all fits together, it sincerely improves the learning experience. The subject matter becomes not 7 distinct chapters of abstract methodology, but instead 7 parts of the same story. You'll know why you're doing things a certain way, and when you read the material in chapter 5, for example, you'll fully and readily understand why you learned chapters 1 thru 4 first, not to mention how the material there fits with the ideas in later parts of the book. Previous reviewers were right, you sincerely can injoy reading parts of this text, if not all of it. The examples are painfully clear even to the uninitiated. I honestly believe that if you cannot learn from this book, there is no hope for you. Take it from me, I'm not a math person at all, and yet I'm getting an A in the course thanks entirely to this book. Following lecture I've gone home, cracked open the text and been able to do the entire homework assignment without taking a single peek at my notes from class. The instruction and examples in the text are truly all that you need to work the problems. Yes, it's THAT good. Proofs abound, but they are easy to follow and really help to enforce concepts and the inter-relation between ideas. I dare say the proofs even help you remember why certain definitions are what they are, rather than the sophmoric method of memorization. This book is a steal at twice the price, do yourself a favor and check it out. Please don't be influenced by poor reviews of the previous "hardback" edition, because the new third edition is nothing like that others have commented. Judge for yourself, skim through it a bookstore first or whatever, but don't pass this up just because some halfwhit that failed the course decided to run his mouth on amazon (see below).
Rating:
Summary: Lay's rep for excellence seems well deserved
Review: I bought this book halfway through a linear algebra course because the professor's lecture notes were terrible and I needed some other reference to study for the final. Its not often that you can legally trade 40 bucks for a decent grade, but this was one of those cases. Lay is a great explainer, and more importantly, his book is arranged for easy referencing. This is the best college math text I've come across.
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